WWII
One theory identifies James J. Kilroy (1902–1962), an American shipyard inspector, as the man behind the signature.[6] James Kilroy had served on the Boston City Council and represented the Roxbury district in the Massachusetts Legislature during the 1930s. He worked at the Fore River Shipyard in Quincy during the war checking the work of riveters paid by how many rivets they installed.[12] Usually, inspectors made a small chalk mark which riveters used to erase, so that they would be paid double for their work. To prevent this, Kilroy marked work he had inspected and approved with the phrase "Kilroy was here" in more durable crayon. It caught on in the European Theater and GIs would scrawl the meme on walls in towns that they advanced through.
https://en.wikipedia.org/wiki/Kilroy_was_here